Relativistic Jets Chechetkin VM 5/28/10 1 Object of simulation - - PowerPoint PPT Presentation

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Relativistic Jets

Chechetkin VM

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Object of simulation

M87 jets (1918)

Radio, X-ray and optical observations 0.8-0.9c, 5·1016 km

SS433 jets (1977)

Picture and radio observation 0.26c, 3·1011 km

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Object of simulation. SS433 in motion: bullets of matter

The VLBA observations Movie (Mioduszewski, Rupen, Walker, & Taylor 2004)

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Object of simulation

Primary properties:

 Various types of objects

(AGNs, microquasars)

 Jets have extremely high

energetics.

 Flow is well collimated

(approx. 10°) and its structure is preserved for large distances

 Flow consists mostly of

individual bullets emitted more or less periodically.

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Main ways of modeling



MHD models

 Resistive MHD (e.g. Chechetkin, Savel’ev, Toropin 1997)  Ideal MHD



Funnel in thick magnetized accretion disk (e.g. Komissarov 2007, 2008);



Flows around thin magnetized accretion disk without external side accretion (e.g. Chechetkin et al 1995, 1997, Pudritz 1997, Ustyugova et al. 1999);



Magnetically channelized outflows around thin magnetized accretion disk (present work).



Models with radiation (Shapiro 1986, Icke 1989, Taijma 1998,

Chechetkin, Galanin, Toropin 1999)



Jets in supernovae( Chechetkin, 1998, 2002,2004, 2006)

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Basic equations of nonrelativistic MHD: where The basic assumption:

(green members describe finite conductivity, red - dissipation)

• equation of state

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V.M. Chechetkin et all , 1995-2010. «A possible mechanism for the formation of molecular flows»

Previous works: MHD mechanism for collimation

Conditions:



Model is described with non-ideal MHD equation system



Accreting to the central body plasma is not magnetized and there is region with homogenous magnetic field around central object.



Due to the non-perfect conductivity of plasma accreting matter diffuses to the magnetic field.

Results:



Along rotation axis of system the accelerating channel (funnel) is formed



Plasma is able to penetrate inside this channel, it is source of jet matter



A series of plasma density discontinuities driving along system axis of rotation obtained

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g r r r

2

• g

F

c

F

• 30

Magnetic monopole 11

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• v

v t t z r v

p p

velocity azimuthal the

• f

lines Level (b) shown. are line) (solid disk the from coming matter the

• f

boundary the and line), dashed (long surface ic magnetoson fast the line), (dashed surface Alfven the line), dashed

• (dot

surface ic magnetoson slow the Also . to al proportion are arrows the

• f

lengths disk.The the

• f

edge inner the

• f

period rotation the

• f

units in measured is where , times,

• f

sequence a at velocity flow Poloidal (a) r K r 24 , , 4 , ) , ( =

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(a) Poloidal magnetic lines. (b) Level lines of the toroidal magnetic field

. collimated well becomes line field the jet,

• f

head the with associated n propagatio twist

• utward

the After , at disk the from starts that line field magnetic a

• f

views l dimentiona

• Three

. 4 = = y r x

i

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1995

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direction in acting Boundary Free" "

• P

B j F r r

( )

Boundary Free"

• Force

" =

• rB

BP r

( )

• B

B B r B

=

• r

r Boundary F.F." " Modified

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( )( ) ( )(

) ( )

velocity casp" "

• where

, : plane

• )

, ( by the cone

• f

section

• cross

is which , 2 angle by sed characteri be can cone Mach

c v c v v c v c v v v c v tg z r + =

• +

=

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r z

Accretion Magnetic field Rotating thin perfectly conducting disk Gravitating central

• bject

Outward boundary

Model scheme

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Results: distribution of density and poloidal magnetic field

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

The channel confined by the magnetic field is stable, and its characteristics vary only weakly with time.



The channel walls are formed of unmagnetized plasma with a high density and pressure. Such walls provide possibilities for accelerating the matter due to the pressure of the central body radiation.

log p

Results: gas pressure logarithm and streamlines

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The jet is well collimated: the channel has the shape of a cone with a non-linear track, whose angle to the z axis is about 10°.



The shape of the channel resembles that of a Laval aerodynamical nozzle. The critical cross section is the region of stagnation of the accreting matter.

Bz

Results: axial magnetic field and streamlines

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Results: instability of magnetic field lines under thin accretion disk (animation of magnetic field poloidal projection)

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hole. black the

• f

mass the

• ,

2 where , hole. black hild Schwardzsc a around field nal gravitatio the describe to Wiita

• Paczynski
• f

ntial pseudopote the use We

2

M c GM r r r GM

g g g

=

• =
• .

) 2 , ( , ) 2 , ( , ) 2 , ( disk. represents hich boundary w

• f

part the

• 2

, 2 3) ; " conditions boundary free " : 2 and , 2 2) ; conditions symmetric : 2 , 1) . conditions Boundary

max max max

= = =

• =

= =

• =
• r

r H r H r r r r r r r r r r

r g g g

r GM r r r r

g keplerian

• =

=

• )

( ) ( field magnetic and density

• f
• ns

Distributi

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Previous works: MHD mechanism for collimation

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Galanin M.P., Toropin Yu.M., Chechetkin V.M. The Radiative Acceleration of Matter Bullets in Accretion Funnels near Astrophysical Objects. (1997)

Previous works: acceleration of matter by radiation pressure

Top speeds of bullets in conic funnel (depends on angle β and absorption coefficient r)

• The null-dimension model including ODE for bullet

dynamics in radiation field considered.

• The existence of channel with hot region at the

foundation makes conditions for individual bullets to be effectively accelerated by radiation and launched out of the system.

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Previous works: radiative acceleration and importance

• f the funnel walls

X – distance between bullet and central

• bject.

V – bullet velocity. Continuous line – acceleration of bullet in the funnel with perfectly reflecting walls. Dotted line – acceleration of bullet without funnel.

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v –velocity of the bubble, с - light speed, Р in..3 и Р ° n. 3 -pressures, which react on the bubble interior and outer face thereafter , G - gravitational constant

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Characterized for radiant pressure on bubble`s wall P n,3 = e3 P 0, e3 = ∆3/∆

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Maximal velocity( v –velocity of the bubble/ с - light speed) r- reflection coeffjcient β – opening angle



Г2

β= 00 β = 3° β = 5° β= 10°

 0.0 0.456 0.486 0.506 0.556  0.2 0.490 0.525 0.547 0.599  0.4 0.532 0.570 0.595 0.648  0.6 0.582 0.626 0.651 0.701  0.8 0.652 0.697 0.721 0.763  0.9 0.700 0.745 0.765 0.800

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0.0 0.151 0.247 0.380 0.467 0.486 0.486 0.3 0.171 0.278 0.427 0.524 0.547 0.547 0.6 0.199 0.323 0.490 0.599 0.625 0.626 0.9 0.251 0.403 0.597 0.713 0.744 0.745 г2 τ= 0.1 0.3 1 3 10 33

Maximal velocity at opening angle ( β= 3°) при χ 3 = 0 (ratio of temperatures) , r3 = r1 =0

0.0 0.486 0.539 0.583 0.619 0.3 0.614 0.673 0.720 0.758 0.6 0.740 0.798 ' 0.841 0.874 r2 rr г3 = 0.0 г3 = 0.3 г3 = 0.6 г3 = 0.9 0.9 0.872 0.918 0.948 0.967

Maximal velocity (β= 3°) при χ 3 = 0.9, τ = 33

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, , , , =

• =
• +
• =
• =

+

• H

E H E j H E t t

• где E(t,x), H(t,x) – электромагнитное поле, f(t,x,p) – функции распределения, v= ðw/ðp -

скорости , w=(m2+p2)1/2 - энергии, m – массы покоя, q – заряды, соответственно, электронов (e) и протонов (p). Плотности заряда и тока

( )

,

, , , , , ,

=

• +

+

• +
• p

H v E x v

p e p e p e p e p e p e

f q f t f

, ,

3 3

p fd q p fd q = = v j

• с суммированием по сортам частиц.

Здесь и далее используется следующая система единиц: длина - L - характерный размер, скорость - c - скорость света, время – L/c , частота – c/L, масса частицы – m - масса покоя электрона, импульс частицы - mc, энергия частицы - mc2, поле - mc2/eL , где e – элементарный заряд концентрация частиц - mc2/4πe2L2, плотность заряда - mc2/4πeL2, число частиц - mc2L/2e2, функция распределения по энергии – L/2e2, энергия - m2c4L/2e2.

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Перераспределение начальной кинетической энергии

электронов Ke0 : Ke - энергия электронов, ΔKp - энергия, переданная протонам, U - энергия электромагнитного поля.

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Электронное облако и протонное ядро на момент t=10

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Распределение Fe(ke) электронов и Fp(kp) протонов по энергиям при t=50

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Протонное ядро (a) и проекции (Pz, r), (Pr, r) фазового портрета протонов (b) на момент t=50.

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Рис.11- проекция облака а) - электронов б) - протонов на плоскость ( r,z) t=100

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• The region of peak intensity of

neutrino ; L = 1053 erg/s Blast wave of SN bubble Potoneutron core of supernova

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Thank you for your attention!